How can a smoke domain be hidden from render?
Your problem with the highlited nodes is that the density is affecting the color, but not the density of the volume.  So all areas of the domain are emitting light (at strength 1.1).

To fix this simply plug the density into a math multiply node to change the overall strength, then plug that into the emission strength.  You could also put it through a color ramp or RGB curves node first to adjust the falloff.



This way the areas of the domain with 0 density will be emitting 0 light as they should.

Without density controlling strength:


With above node setup: